Set-valued fractional programming problems with $ \sigma $-arcwisely connectivity

Koushik Das; Savin Treanţă; Muhammad Bilal Khan; Koushik Das; Savin Treanţă; Muhammad Bilal Khan

doi:10.3934/math.2023666

AIMS Mathematics

2023, Volume 8, Issue 6: 13181-13204. doi: 10.3934/math.2023666

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Research article

Set-valued fractional programming problems with $ \sigma $-arcwisely connectivity

1.
Department of Mathematics, Taki Government College, Taki 743429, West Bengal, India
2.
Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania
3.
Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest, Romania
4.
Fundamental Sciences Applied in Engineering-Research Center (SFAI), University Politehnica of Bucharest, 060042 Bucharest, Romania
5.
Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, Pakistan

Received: 31 October 2022 Revised: 12 March 2023 Accepted: 23 March 2023 Published: 03 April 2023
MSC : 26B25, 49N15

In this paper, we determine the sufficient Karush-Kuhn-Tucker (KKT) conditions of optimality of a set-valued fractional programming problem (in short, SVFP) $\rm (FP)$ under the suppositions of contingent epidifferentiation and $ \sigma $-arcwisely connectivity. We additionally explore the results of duality of parametric $\rm (PD)$, Mond-Weir $\rm (MWD)$, Wolfe $\rm (WD)$, and mixed $\rm (MD)$ kinds for the problem $\rm (FP)$.
- set-valued map,
- convex cone,
- contingent epidifferentiation,
- duality
Citation: Koushik Das, Savin Treanţă, Muhammad Bilal Khan. Set-valued fractional programming problems with $ \sigma $-arcwisely connectivity[J]. AIMS Mathematics, 2023, 8(6): 13181-13204. doi: 10.3934/math.2023666

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Abstract

In this paper, we determine the sufficient Karush-Kuhn-Tucker (KKT) conditions of optimality of a set-valued fractional programming problem (in short, SVFP) $\rm (FP)$ under the suppositions of contingent epidifferentiation and $ \sigma $-arcwisely connectivity. We additionally explore the results of duality of parametric $\rm (PD)$, Mond-Weir $\rm (MWD)$, Wolfe $\rm (WD)$, and mixed $\rm (MD)$ kinds for the problem $\rm (FP)$.

References

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